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Application of Threshold Regressive Model to Predicting Annual Runoff

JIN Ju-liang, YANG Xiao-hua, JIN Bao-ming, DING Jing (Sichuan University, Chengdu Sichuan 610065, China) (Hehai University, Nanjing Jiangsu 210098, China) (Water Electricity, Bureau of Nanping, Naping Fujian 353000, China)  
Today water is in great demand. The variation in annual runoff not only influences economy and people's standards of living, but also curbs the economic development. To solve these problems, accurately predicting the variation of annual runoff is indispensable to scientifically utilize water resources. Being the output of a rainfall-runoff system. the annual runoff time series is a complex dynamic phenomenon variating from region to region and changing with time, which includes lots of past information of all variations and hides many laws. Treads of system evolution are often time irreversible. non-linear with weak dependence. Traditional methods for predicting annual runoff usually use linear technology, but the forecasting precision is dissatisfactory, owing to complexity of its intrinsic evolutions, and its close and complicated relationships to climate change and other effect factors. In order to effectively utilize the important information of the section dependence during the time series of annual runoff and its effect factors, and to increase annual runoff forecasting precision, Threshold Regressive (called TR for short) model based on genetic algorithm is suggested to describe and predict annual runoff in this paper. Genetic algorithm is a kind of general optimization methods based on the mechanics of natural selection and natural genetics. which is a general approach to optimization of parameters of non-linear models. A simple and general scheme is presented for establishing TR model with the improved genetic algorithm, named accelerating genetic algorithm (called AGA for short) developed by the authors. Both threshold values and regressive coefficients can be optimized conveniently by using AGA. and the difficulty of TR model is resolved. which gives a strong tool for widely applying TR model to predict non-linear time series. The scheme includes three steps as follows: 1) To determine the regressive items of TR model and the delay time steps by using the technique of correlation analysis. 2) To determine the number of threshold sections and the search ranges of threshold values by using scatter dot figure. 3) To optimize the parameters of TR model based on the criterion of minimizing the fitting errors between TR computed values and observed values of annual runoff by using the improved genetic algorithm. A case study shows that the scheme is simple, practical and efficient. and that TR model can successfully reduce model errors, and can ensure good stability and forecasting accuracy of the model by controlling threshold valves. The scheme can also be applied to mid and long-term prediction in other natural resources.
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